Section 7.8, due on November 15

The most difficult part of this material for me was understanding the Third Isomorphism Theorem and the theory that lead up to it. I still don't think I fully understand what subgroups of G/N look like and how they are related to G. I am also still a little confused about the section where they talk about how simple groups are the building blocks of all other groups and also the term composition factors.

The most interesting part of this section for me was theorem 7.45. I thought this was interesting considering that simple groups are the building blocks for all other groups and we know what the building blocks are isomorphic to, but when combined into a larger group we do not always know.